Ordinary Differential Equations and Stability Theory: An Introduction

Ordinary Differential Equations and Stability Theory: An Introduction

by David A. Sanchez



Product Details

ISBN-13: 9780486638287
Publisher: Dover Publications
Publication date: 02/29/2012
Pages: 192
Product dimensions: 5.70(w) x 8.19(h) x 0.41(d)

Table of Contents

Chapter I. Introduction
  1.1 Preliminary Notation
  1.2 The Ordinary Differential Equation
  1.3 An Existence and Uniqueness Theorem
  1.4 The Maximum Interval of Existence
Chapter 2. The Linear Equation: General Discussion
  2.1 Introduction
  2.2 Fundamental Solutions
  2.3 The Wronskian
  2.4 The Nonhomogeneous Linear Equation
  2.5 The nth-Order Linear Equation
  2.6 The Nonhomogeneous nth-Order Linear Equation
Chapter 3. The Linear Equation with Constant Coefficients
  3.1 The nth-Order Linear Equation
  3.2 The Nonhomogeneous nth-Order Linear Equation
  3.3 The Behavior of Solutions
  3.4 The First-Order Linear System
Chapter 4. Autonomous Systems and Phase Space
  4.1 Introduction
  4.2 Linear Systems—Constant Coefficients
  4.3 A General Discussion
  4.4 Nonlinear Systems
Chapter 5. Stability for Nonautonomous Equations
  5.1 Introduction
  5.2 Stability for Linear Systems
  5.3 Two Results for Nonlinear Systems
  5.4 Liapunov's Direct Method
  5.5 Some Results for the Second-Order Linear Equation
Chapter 6. Existence, Uniqueness, and Related Topics
  6.1 Proof of the Existence and Uniqueness of Solutions
  6.2 Continuation of Solutions and the Maximum Interval of Existence
  6.3 The Dependence of Solutions on Parameters and Approximate Solutions
Appendix A. Series Solutions of Second-Order Linear Equations
Appendix B. Linear Systems with Periodic Coefficients
  References; Index

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